Limit cycles for a generalization of polynomial Liénard differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

Date:	2013
Abstract:	We study the number of limit cycles of the polynomial differential systems of the form x˙ = y − f1(x)y, y˙ = −x − g2(x) − f2(x)y, where f1(x) = εf11(x) + ε2f12(x) + ε3f13(x), g2(x) = εg21(x) + ε2g22(x) +ε3g23(x) and f2(x) = εf21(x)+ε2f22(x)+ε3f23(x) where f1i, f2i and g2i have degree l, n and m respectively for each i = 1, 2, 3, and ε is a small parameter. Note that when f1(x) = 0 we obtain the generalized polynomial Liénard differential systems. We provide an accurate upper bound of the maximum number of limit cycles that this differential system can have bifurcating from the periodic orbits of the linear center ˙x = y, ˙y = −x using the averaging theory of third order.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Polynomial differential systems ; Generalized Liénard system
Published in:	Chaos, solitons and fractals, Vol. 46 (2013) , p. 65-74, ISSN 0960-0779

DOI: 10.1016/j.chaos.2012.11.010

Postprint 28 p, 735.5 KB

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